Summer 2005
University of Denver
Mathematics Alumni
Newsletter
Inside this issue:
A Note From Jim Hagler
Visit the Mathematics
Department Web Site
at
www.math.du.edu
A Note From Jim Hagler
1
Conference on Quasigroups,
Loops, and Nonassociative
Systems
1
Memories of Prof. Recht
2
Where Are They Now?
2
Dr. Arthur Lewis, Sr.
3
Math Puzzler
3
Who Was John Greene?
4
This newsletter is
published semiannually
and your submissions
are welcome.
If you have an article, a picture, or
information that might be of interest to
other alumni and you would like to
have it published in the newsletter,
please send it to:
Don Oppliger
DU Math Dept
2360 S. Gaylord
Denver, CO 80208
[email protected]
Please include your name, mailing
address, and email address so we
can contact you.
This newsletter may be
read on-line at
www.math.du.edu
If you would prefer to receive an
email notification when each edition
is published rather than a printed
copy, please let us know by sending an email to [email protected].
In this newsletter, we continue to “look back” at some of the history of the Department of Mathematics. Previously (Winter 2005) we featured excerpts from articles by Professor Albert Recht,
chair of the math department in 1943-44 and 1947-49. These articles were the catalyst for a number of letters and e-mails from alumni, which contained
both their memories of Professor Recht and updates on
their own lives. Among these was a recollection (page 2)
by Dr. Arthur Lewis, Jr., who mentioned that his father, Dr.
Arthur Lewis, Sr. had also been a member of the department. In response to our request for more information
about his father, he sent us the very nice letter which appears on page 3. His daughter was kind enough to provide us the picture reproduced here.
A second reason to look back is due to a recurring question: “Who was John Greene?” (The department has been
housed in John Greene Hall for more than 40 years.) My
thanks to Don Oppliger, (whose primary job is to work with
TAs and direct Foundations Labs) who pursued the answer to this question. We are pleased to provide some
details on page 4.
Dr. Arthur Lewis Sr. and Maude Lewis
Conference on Quasigroups, Loops, and
Nonassociative Systems
On July 2 through July 9, 2005, the University of Denver Mathematics Department hosted the
Mile High Conference on Quasigroups, Loops, and Nonassociative Systems. The conference
focused on recent results in nonassociative mathematics, in particular on quasigroups and loops.
Contributions from related areas (nonassociative algebras, Latin squares, and computational
systems for nonassociative mathematics) were also received.
Invited speakers for the conference included Michael Aschbacher (Cal Tech, USA), Orin Chein
(Temple U, USA), Patrick Dehornoy (U de Caen, France), Aleš Drápal (Charles U, Czech Republic), Michael Kinyon (Indiana U, South Bend, USA), and William McCune (Argonne National
Laboratory, USA).
The conference was a great success thanks in large part to the hard work of local organizers Dr.
Petr Vojtĕchovský, Dr. Nic Ormes, and graduate student Dan Daly, as well as the other graduate
students who provided support, Mohammed Al-Bow, Melissa Butler, Jeff Edgington, Kyle Pula,
Jonathan Von Stroh, and Brett Werner. Many thanks to these people.
In addition to hearing the conference presentations, the participants enjoyed an outing to the
Garden of the Gods in Colorado Springs and the Cave of the Winds in Manitou Springs.
A photo from the conference appears on Page 4 of this newsletter and a post-conference Web
site at www.math.du.edu/milehigh provides a summary of information about the conference.
Memories of Professor Recht
A number of alumni provided us their memories of Dr. Recht as well
as updates about themselves.
From John Adams (BA, 1946) - “It was with interest I received the article about one of my favorites, Albert Recht. One day
before class (1945) he was demonstrating skill as a high jumper. I helped him up from the floor, he dusted off, and started the
lecture. DU was certainly a full service university for me as it gave me a degree, found me a wonderful wife (58 years), and provided the minister, our friend Walter Sikes (Economics Professor/Minister), all in one year.”
From Aubrey Speer (BA, 1943) - “I always enjoy the math newsletters. Especially enjoyed the article about Dr. Recht. He
was my Astronomy Professor and I fulfilled my duties for my assistantship by doing some astronomical calculations on a very old
computer. My major was math and my math professors were Prof. Gorrel and Dr. Stearns. My minors were Geology and Education. I did my student teaching at a high school close enough to the campus to walk there, but I never did teach. In those days it
was Tramway Tech and most of the students came from Denver. I lived in one of the original dorms and still participate in a
Round Robin with 5 others who lived in the same dorm. My first job after DU was with the time study dept. at RCA in Camden,
NJ. It was interesting and challenging but I preferred this part of the country. I went to work as a Geophysical Computer for Cities
Service Oil Co. in Houston, TX. Married there and became a housewife and mother. Lived in Muskogee, OK, Washington DC,
Dallas, Shawnee Mission, KS (a suburb of Kansas City), and now in a Retirement Community called John Knox. Still happily married after 56 years. Four children. The oldest graduated from Oklahoma City University and has a daughter at DU now. (name is
Bethany Speer ). Next is a daughter who lives in a nearby suburb. The daughter graduated from KU and is in Human Relations.
Next daughter lives in Lawrence and attended KU. She is a pretty good artist and has done a great job of raising 7 kids. Oh yes,
the son in OK City is a business major and a land man for an oil co. The youngest graduated from Rolla as a geological engineer,
He lives in Midland, TX and does independent contracting for an oil man (That means finding the oil, being his own business
manager and supervising drilling.) He also does advisory work on computers.”
From Arthur Lewis, Jr. (BA, 1940) - “Your Newsletter article on Albert W. Recht brought back a host of memories. When I
attended DU (1936-1940) there were three members in the Math Department: Professor Gorrell, Professor Albert Recht and my
father, Professor Arthur Lewis. Professor Recht and father were good friends and together they taught me the art of catching trout
on a dry fly in cold mountain streams.
“I worked as a student assistant with Professor Recht at the Chamberlin Observatory. Later I worked with Professor Recht as he
completed his doctoral dissertation at the University of Chicago. The dissertation involved computing the path of a comet through
the solar system and determining when and where it would become visible. Professor Recht developed formulas based on the
gravitational attraction of the sun and the nearby planets that enabled him to chart the position of the comet for every ten day
period over a number of years. To make a single calculation required the use of a hand operated calculating machine and took
about twelve minutes. Today the orbit could be computed by a computer in a matter of seconds, or minutes at the most. Professor
Recht was under a great deal of time pressure since he had to complete his work before the comet became visible. He, another
student and I worked around the clock and completed the work. The comet arrived as Recht had predicted, on time and at the
correct location. Professor Recht became Dr. Recht.
“As I started my teaching career, as a colleague of Ruth Hoffman at North High School in Denver, I tried to emulate two of Professor Recht’s outstanding attributes as a teacher. His lectures emphasized the use of reasoning in deriving mathematical formulas
and his examination questions required reasoning rather that rote memory. Another attribute of Professor Recht’s teaching was
his use of humor. For example, he told us, ‘The moon affects the tide as well as the untied!’ (That was humor, circa 1938).
“When I became principal of University Park Elementary School (1947-1949), two of Dr. Recht’s children attended the school.
Later I became Director of Instruction in the Denver Public Schools and Assistant Superintendent in the Minneapolis Schools
(1952-1962). I was a professor at Teachers College, Columbia University (1962-1970) and at the University of Florida until I retired in 1984.”
Where Are They Now?
Bill Johnson (BA 1964) provided us with the following update about his activities since
leaving DU. “I am a 1964 graduate of DU. Taught math for several years in public
schools in Iowa and in Oregon. Have been an administrator in education for more than 35 years, and a Superintendent of a School
for the Deaf for some 29 years. Retired, and was brought out of retirement six months later to head another school for deaf individuals. I happened to be one of the very few deaf individuals who graduated from DU. The early 1960’s were a time when interpreters,
notetakers, tutoring, etc. were unknown provisions of service.”
We always like to get news from our alumni. Send us a paragraph or two and let us know what you have been doing. Send information to: Don Oppliger, DU Math Dept., 2360 S. Gaylord, Denver, CO 80208 or email to: [email protected]
Dr. Arthur Lewis, Sr.
After we received the
letter (Page 2) from
Arthur Lewis, Jr. that
mentions his father as a math faculty member at DU, we decided we would
like to know more about Dr. Lewis, Sr. We asked his son to tell us more and
he responded with the information below.
“In regard to your request for history regarding members of the
Mathematics Department, I submit the following brief history of my
father as well as a very brief comment about another member of
the department, Professor Russell.
“The grandparents of Professor Arthur Lewis were real pioneers. They crossed the prairie in a covered wagon and homesteaded land near Golden, Colorado in 1859. Prof. Lewis grew up
on a farm situated midway between Denver and Golden on West
44th. He graduated from the University of Denver with a B.A. major in mathematics. He then taught in the DU Demonstration High
School while completing his M.A. degree in mathematics at the
University of Denver, graduating in June of 1907. His first teaching
position was as a mathematics teacher in Denver's North High
School. From there he went to Albion, Idaho, to teach in Albion
State Normal School for two years. His next teaching position was
in the La Crosse Wisconsin Normal School. Then he returned to
his father's farm in Wheatridge, Colorado, during World War I. He
explained his reason for doing this in a letter he wrote to Chancellor
Hunter that is quoted in a Memorial for Arthur J. Lewis passed by
the University of Denver Senate in 1961.
The Carnegie Library and Buchtel Memorial Chapel as they appeared
in 1917, The one tower of the chapel that still stands on campus can
be seen. The remainder of the chapel burned down in 1983.
Math Puzzler
“Professor Lewis began his teaching career at the University of
Denver in September of 1926. He was hired by Dr. Russell the
Chairman of the Mathematics Department. Dr. Russell had
been one of Professor Lewis's teachers and supervised his
student teaching. Since you are interested in the history of
members of the Math. Dept., let me insert a brief note regarding Dr. Russell. Sometime in the early 1930s I accompanied
my parents and siblings for a Saturday visit to the mountain
cabin of Dr. and Mrs. Russell. I was very impressed with their
beautiful mountain cabin and their new Pierce Arrow car. (The
Pierce Arrow touring car was a luxury vehicle for its time.) We
returned home on Saturday. When, on the following day, Dr.
and Mrs. Russell were returning home their new Pierce Arrow
stalled on the railroad tracks on Evans Avenue near South
Broadway. A train was coming. Mrs. Russell got out of the car
but Dr. Russell kept trying to start his new car. Unfortunately,
Dr. Russell was killed when the train hit his car.
“After accepting a position at the University of Denver, Professor Lewis started to work on a Ph D. degree at the University
of Colorado in Boulder. When he was ready to start work on
his dissertation he explained to me, ‘You know a doctoral thesis is supposed to be an original piece of research that adds
something new to the field. I am having trouble because almost everything there is to know about mathematics has already been discovered.’ The title of his dissertation was "The
Solution of Algebraic Equations with One Unknown Quantity
by Infinite Series." The University of Colorado awarded him
the Ph.D. Degree in August of 1932.
“The three members of the department, Prof. Recht, Prof. Gorrell and Prof. Lewis ‘took turns’ serving as Chairman of the
Department. Professor Lewis was particularly interested in
teaching advanced courses on the theory of numbers. He was
very intrigued with possible applications of the binary number
system. One hallmark of his teaching was that if the class
were making satisfactory progress, the Friday session was
devoted to what he called ‘recreational math.’ In retrospect, I
now realize that he was really engaging students in higher
order thinking camouflaged as recreational mathematics.
(Continued on page 4)
The previous puzzler asked … Suppose Player A has n+1 coins while Player B has n coins. Both
players toss all of their coins simultaneously and observe the number that come up heads. Assuming all
of the coins are fair, what is the probability that A obtains more heads than B?
Solution: The solution lies in the observation that, since A has only one extra coin, A must either throw more heads than B or A must
throw more tails than B, but cannot do both. By symmetry, these two mutually exclusive possibilities occur with equal probability and the
probability that A obtains more heads than B is 1/2. (Helen Nielsen (MS, 1976) sent us a correct response to this puzzler.)
For the next puzzler … A cylinder 48 cm high has a circumference of 16 cm. A string makes exactly 4 complete turns
around the cylinder while its two ends touch the cylinder's top and bottom as shown in the figure to the right. How long is
the string in cm?
Send answers to [email protected]
Dr. Arthur Lewis, Sr.
(Continued from page 3)
“Professor Lewis had interests that extended beyond the field of mathematics and that led to
other ways to serve the University. He was a sport enthusiast,
both as a participant and as a spectator. He served on the faculty
committee for athletics for many years and coached the men's
Who Was John Greene?
tennis team as a volunteer activity. His interest in the game of
chess led him to organize a chess club at the University.
“Like any good teacher, Professor Lewis took a great interest in
the welfare of his students. At the 50th reunion of the class of
1940, many of my fellow alumni told of the significant role Prof.
Lewis had played in their lives.”
Many, many thanks to Kathy Mitchell, an Archives Specialist in the DU Penrose Library who
was instrumental in identifying and collecting material about Dr. Greene. Also, thanks to James
Armstrong who was visiting DU for his daughter Clare’s graduation and who gave us interesting information about John Greene that helped pique our
curiosity to learn more about the man.
The information provided below was taken from two sources found in the archives of the Penrose
Library. The first was some short biographical material and the second was a document entitled Conversation between Randolph McDonough (Director of Alumni Relations, 1929-58) and Dr. Alfred C.
Nelson (Interim Chancellor, 1948-49) on Campus Buildings, Their Namesakes and Histories, with
Patricia Dublin, University of Denver Alumni Relations. Anybody interested in learning more is encouraged to read the full text of these documents. We have posted these on the Web and they can
be found by going to the department Web site, www.math.du.edu, clicking on Departmental Life, and
then clicking on the links to the Dr. Greene documents shown under the Summer 2005 Newsletter
heading.
Dr. John W. Greene was a native of Seattle Washington. He obtained his BS degree in Chemical
Engineering from the University of Washington, his MS from the Carnegie Institute of Technology,
and his doctorate from the University of Pittsburg. After several years of fundamental research in industry, he joined the faculty of Kansas State and became head of the Chemical Engineering Department in 1942. He came to Denver in 1946 as Chairman of the Chemical Engineering Department
where he earned the highest regard of his colleagues and students. On May 22, 1948, Dr. Greene
Dr. John W. Greene
and his colleague at DU, Ralph Conrad, were killed in a tragic rafting accident on the South Platte
River near Deckers. When John Greene Hall was built in 1958, it was named as a memorial to Dr. Greene. Conrad Hall (no longer
here) was named to honor Conrad.
Other interesting information to come out of this research was the fact that John Greene Hall was originally a two-story building and a
third floor was subsequently added. The cost of the building has been reported as $239,912. It isn’t clear whether or not this includes
the reported amount of $54,000 for the third floor.
Attendees at the July Conference on Quasigroups, Loops, and Nonassociative Systems.